Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator
An optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. First, the dynamic model of the nonlinear structure considering the dynamics of a piezoelectric stack inertial actuator is established, and the motion equat...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2020/5372045 |
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| author | Q. F. Lü X. F. Wang K. Lu R. H. Huan |
| author_facet | Q. F. Lü X. F. Wang K. Lu R. H. Huan |
| author_sort | Q. F. Lü |
| collection | DOAJ |
| description | An optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. First, the dynamic model of the nonlinear structure considering the dynamics of a piezoelectric stack inertial actuator is established, and the motion equation of the coupled system is described by a quasi-non-integrable-Hamiltonian system. Then, using the stochastic averaging method, this quasi-non-integrable-Hamiltonian system is reduced to a one-dimensional averaged system for total energy. The optimal control law is determined by establishing and solving the dynamic programming equation. The proposed control law is analytical and can be fully executed by a piezoelectric stack inertial actuator. The responses of optimally controlled and uncontrolled systems are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation to evaluate the control effectiveness of the proposed strategy. Numerical results show that our proposed control strategy is effective for random vibration reduction of the nonlinear structures using piezoelectric stack inertial actuator, and the theoretical method is verified by comparing with the simulation results. |
| format | Article |
| id | doaj-art-6b6f06df73424e79b31336d795db9064 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-6b6f06df73424e79b31336d795db90642025-02-03T05:52:42ZengWileyShock and Vibration1070-96221875-92032020-01-01202010.1155/2020/53720455372045Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial ActuatorQ. F. Lü0X. F. Wang1K. Lu2R. H. Huan3Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, ChinaAn optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. First, the dynamic model of the nonlinear structure considering the dynamics of a piezoelectric stack inertial actuator is established, and the motion equation of the coupled system is described by a quasi-non-integrable-Hamiltonian system. Then, using the stochastic averaging method, this quasi-non-integrable-Hamiltonian system is reduced to a one-dimensional averaged system for total energy. The optimal control law is determined by establishing and solving the dynamic programming equation. The proposed control law is analytical and can be fully executed by a piezoelectric stack inertial actuator. The responses of optimally controlled and uncontrolled systems are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation to evaluate the control effectiveness of the proposed strategy. Numerical results show that our proposed control strategy is effective for random vibration reduction of the nonlinear structures using piezoelectric stack inertial actuator, and the theoretical method is verified by comparing with the simulation results.http://dx.doi.org/10.1155/2020/5372045 |
| spellingShingle | Q. F. Lü X. F. Wang K. Lu R. H. Huan Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator Shock and Vibration |
| title | Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator |
| title_full | Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator |
| title_fullStr | Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator |
| title_full_unstemmed | Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator |
| title_short | Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator |
| title_sort | nonlinear stochastic optimal control using piezoelectric stack inertial actuator |
| url | http://dx.doi.org/10.1155/2020/5372045 |
| work_keys_str_mv | AT qflu nonlinearstochasticoptimalcontrolusingpiezoelectricstackinertialactuator AT xfwang nonlinearstochasticoptimalcontrolusingpiezoelectricstackinertialactuator AT klu nonlinearstochasticoptimalcontrolusingpiezoelectricstackinertialactuator AT rhhuan nonlinearstochasticoptimalcontrolusingpiezoelectricstackinertialactuator |